Main Analysis
Data Background Information
Treatment Averaged Data
| Sample_Number | Sedum.rubro | Sedum.acre | bare.substrate | rubro.vs.acre | rubro.vs.substrate | acre.vs.substrate | hour | timestamp | day |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 23.00 | 25.17 | 25.50 | -2.17 | -2.50 | -0.33 | 14 | 2019-03-04 14:18:00 | 2019-03-04 |
| 2 | 24.17 | 23.33 | 25.00 | 0.83 | -0.83 | -1.67 | 14 | 2019-03-04 14:48:00 | 2019-03-04 |
| 3 | 24.83 | 23.50 | 25.00 | 1.33 | -0.17 | -1.50 | 15 | 2019-03-04 15:18:00 | 2019-03-04 |
| 4 | 24.50 | 23.33 | 24.83 | 1.17 | -0.33 | -1.50 | 15 | 2019-03-04 15:48:00 | 2019-03-04 |
| 5 | 22.67 | 21.50 | 22.83 | 1.17 | -0.17 | -1.33 | 16 | 2019-03-04 16:18:00 | 2019-03-04 |
| 6 | 20.33 | 18.83 | 20.00 | 1.50 | 0.33 | -1.17 | 16 | 2019-03-04 16:48:00 | 2019-03-04 |
All Cells Data
| Sample | Temp | Location | Cell | TimeStamp | Ambient | Treatment |
|---|---|---|---|---|---|---|
| 1 | 20.178 | exterior | 1 | 2019-04-03T21:18:00Z | 15.55556 | sedum rubrotinctum |
| 2 | 19.177 | exterior | 1 | 2019-04-03T21:48:00Z | 15.00000 | sedum rubrotinctum |
| 3 | 18.676 | exterior | 1 | 2019-04-03T22:18:00Z | 15.00000 | sedum rubrotinctum |
| 4 | 17.675 | exterior | 1 | 2019-04-03T22:48:00Z | 14.44444 | sedum rubrotinctum |
| 5 | 15.672 | exterior | 1 | 2019-04-03T23:18:00Z | 14.44444 | sedum rubrotinctum |
| 6 | 15.672 | exterior | 1 | 2019-04-03T23:48:00Z | 13.88889 | sedum rubrotinctum |
Comparison of Treatment Avgerages
| comparison | mean(difference) | max(difference) | sd(difference) |
|---|---|---|---|
| rubro vs substrate | -0.0022 | 5.5 | 0.5922 |
| acre vs substrate | -0.4686 | 4.0 | 0.8532 |
Temperature Differences by Hour
| counts | rubro - substrate | Percent (%) rubro |
|---|---|---|
| negative/colder | 615 | 36.607 |
| positive/hotter | 507 | 30.179 |
| zero/same | 558 | 33.214 |
| counts | acre - substrate | Percent (%) acre |
|---|---|---|
| negative/colder | 1355 | 80.650 |
| positive/hotter | 181 | 10.770 |
| zero/same | 144 | 8.571 |
Comparison of Temperatures by Hour
Daily Range, Max, and Min
Diurnal Temperature Ranges (DTR)
| mean(rubro_range) | mean(acre_range) | mean(soil_range) |
|---|---|---|
| 17.5258 | 16.6522 | 18.0258 |
Daily Max Temperatures
| Category | rubro_max | acre_max |
|---|---|---|
| Lower Max (vs Soil) | 34.000 | 33.000 |
| Higher Max (vs Soil) | 1.000 | 2.000 |
| Same Max (vs Soil) | 1.000 | 1.000 |
| Average Max Temperature | 29.124 | 27.958 |
| Maximum Max Temperature | 38.000 | 36.330 |
Daily Min Temperatures
| Category | rubro_max | acre_max |
|---|---|---|
| Lower Min (vs Soil) | 5.000 | 32.000 |
| Higher Min (vs Soil) | 11.000 | 2.000 |
| Same Min (vs Soil) | 20.000 | 2.000 |
| Average Min Temperature | 11.598 | 11.306 |
| Minimum Min Temperature | 8.000 | 7.500 |
Paired T-Tests - DTR, Max, and Min
| t_test | p_value | CI_Lower | CI_Upper |
|---|---|---|---|
| rubro DTR | 0.0000 | -0.5860 | -0.4140 |
| acre DTR | 0.0000 | -1.6483 | -1.0989 |
| rubro max | 0.0000 | -0.5515 | -0.3841 |
| acre max | 0.0000 | -1.9150 | -1.3533 |
| rubro min | 0.1119 | -0.0079 | 0.0723 |
| acre min | 0.0000 | -0.3226 | -0.1985 |
Linear Models for Treatment vs Control
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | -0.2214 | 0.0396 | -5.5867 | 0 |
| Sedum.rubro | 1.0121 | 0.0020 | 506.5620 | 0 |
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | -0.6477 | 0.0513 | -12.6341 | 0 |
| Sedum.acre | 1.0619 | 0.0027 | 399.2741 | 0 |
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 18.4963 | 0.1728 | 107.0573 | 0 |
| rubro.vs.substrate | -2.7651 | 0.2918 | -9.4758 | 0 |
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 16.1856 | 0.1647 | 98.2518 | 0 |
| acre.vs.substrate | -4.9446 | 0.1693 | -29.2102 | 0 |
When Ambient > 25 degrees C (Interior T)
| Treatment | count | max | min | range | mean | median | sd |
|---|---|---|---|---|---|---|---|
| bare substrate | 132 | 39.5 | 15.5 | 24.0 | 26.4470 | 28.25 | 8.9522 |
| sedum acre | 132 | 37.5 | 15.5 | 22.0 | 25.7652 | 28.75 | 8.3624 |
| sedum rubrotinctum | 132 | 39.0 | 15.5 | 23.5 | 26.4545 | 29.25 | 8.7805 |
Normality Tests
##
## Shapiro-Wilk normality test
##
## data: treat_avg$Sedum.rubro
## W = 0.92072, p-value < 2.2e-16
##
## Shapiro-Wilk normality test
##
## data: treat_avg$Sedum.acre
## W = 0.92854, p-value < 2.2e-16Data Transformations
Sedum rubrotinctum Transformations
| Transformation Type | Skewness | Kurtosis |
|---|---|---|
| No Transformation | 0.7340 | -0.514 |
| Square Root | 0.4770 | -0.824 |
| Cube Root | 0.3880 | -0.887 |
| Log | 0.2020 | -0.947 |
| Tukey’s Ladder of Powers | -0.0796 | -0.863 |
| Box-Cox | 0.0340 | -0.921 |
Sedum acre Transformations
| Transformation Type | Skewness | Kurtosis |
|---|---|---|
| No Transformation | 0.6960 | -0.532 |
| Square Root | 0.4350 | -0.836 |
| Cube Root | 0.3450 | -0.895 |
| Log | 0.1600 | -0.945 |
| Tukey’s Ladder of Powers | -0.0755 | -0.874 |
| Box-Cox | 0.0264 | -0.922 |
Appendix - Code
#setup and cleaning data
library("tidyverse")
library("ggpubr")
library("scales")
library("MASS")
library("viridis")
library("DT")
library("rcompanion")
library("car")
library("e1071")
library("visdat")
library("gridExtra")
setwd("/Users/edenaxelrad/Desktop/Green Roofs (Thesis)/Run 1 CSV Files")
all_cells <- read.csv("all_cells.csv")
timestamps <- read.csv("sample time-stamps.csv")
timestamps <- timestamps[1:1680,]
timestamps$TimeStamp <- as.POSIXct(timestamps$TimeStamp, format = "%m/%d/%y %H:%M:%S")
timestamps$Time <- format(as.POSIXct(timestamps$TimeStamp,"%m/%d/%y %H:%M:%S"),'%H')
timestamps$Date <- as.Date(timestamps$Date, format = "%m/%d/%y")
treat_avg <- read.csv("treat avg comp.csv", stringsAsFactors = FALSE)
treat_avg <- treat_avg[-1681,]
treat_avg$hour <- timestamps$Time
treat_avg$timestamp <- timestamps$TimeStamp
treat_avg$day <- as.Date(timestamps$Date)
#addressing missing values due to time change
treat_avg[265,8] <- "02"
treat_avg[266,8] <- "02"
treat_avg[265,9] <- "2019-03-10 02:18:00"
treat_avg[266,9] <- "2019-03-10 02:48:00"
#Background information for treatment averaged data
head <- head(treat_avg)
knitr::kable(head, caption = "Data Headers and Sample Records")
ggplot(treat_avg) + theme_void()
#Background information for all cells data
head <- head(all_cells)
knitr::kable(head, caption = "Data Headers and Sample Records")
rubro <- cbind.data.frame(timestamps$TimeStamp, treat_avg$Sedum.rubro, "Sedum rubrotinctum")
colnames(rubro) <- c("Date", "Temperature", "Treatment")
acre <- cbind.data.frame(timestamps$TimeStamp, treat_avg$Sedum.acre, "Sedum acre")
colnames(acre) <- c("Date", "Temperature", "Treatment")
soil <- cbind.data.frame(timestamps$TimeStamp, treat_avg$bare.substrate, "Bare substrate")
colnames(soil) <- c("Date", "Temperature", "Treatment")
treat_temps <- rbind.data.frame(rubro, acre, soil)
ggplot(treat_temps, aes(Date, Temperature, color = Treatment)) +
geom_path() + facet_grid(Treatment ~ .) +
theme(legend.position = "none") +
ggtitle("Temperature by Treatment")
ggplot(treat_avg) + theme_void()
# Comparison of Treatment Avg at Samples
rubro <- cbind(treat_avg$rubro.vs.substrate, "rubro vs substrate")
colnames(rubro) <- c("difference", "comparison")
acre <- cbind(treat_avg$acre.vs.substrate, "acre vs substrate")
colnames(acre) <- c("difference", "comparison")
plot(treat_avg$Sample_Number, treat_avg$rubro.vs.substrate, type = "l",
main = "sedum rubrotinctum - bare substrate",
xlab = "sample number",
ylab = "temperature difference (C)")
abline(h=0, col="blue")
abline(h=mean(treat_avg$rubro.vs.substrate), col="red", lty = 2)
plot(treat_avg$Sample_Number, treat_avg$acre.vs.substrate, type = "l",
main = "sedum acre - bare substrate",
xlab = "sample number",
ylab = "temperature difference (C)")
abline(h=0, col="blue")
abline(h=mean(treat_avg$acre.vs.substrate), col="red", lty = 2)
long_data <- rbind.data.frame(rubro, acre)
long_data$difference <- as.numeric(as.character(long_data$difference))
long_data$abs_diff <- lapply(long_data$difference, abs)
summ_stats <-
long_data %>%
group_by(comparison) %>%
summarize(mean(difference), max(difference), sd(difference))
knitr::kable(summ_stats, digits = 4, caption = "Table: Summary Statistics")
# Temperature Differences by Hour
neg_counts <- c("negative/colder", sum(treat_avg$rubro.vs.substrate<0), sum(treat_avg$acre.vs.substrate<0))
pos_counts <- c("positive/hotter", sum(treat_avg$rubro.vs.substrate>0), sum(treat_avg$acre.vs.substrate>0))
zero_counts <- c("zero/same", sum(treat_avg$rubro.vs.substrate==0), sum(treat_avg$acre.vs.substrate==0))
diff_counts <- rbind.data.frame(neg_counts, pos_counts, zero_counts)
colnames(diff_counts) <- c("counts", "rubro - substrate", "acre - substrate")
diff_counts$`rubro - substrate` <- as.numeric(as.character(diff_counts$`rubro - substrate`))
diff_counts$`acre - substrate` <- as.numeric(as.character(diff_counts$`acre - substrate`))
diff_counts <-
diff_counts %>%
mutate("Percent (%) rubro" = signif(100*(`rubro - substrate`/1680), digits=5)) %>%
mutate("Percent (%) acre" = signif(100*(`acre - substrate`/1680), digits=4))
diff_countsR <- diff_counts[,c(1,2,4)]
diff_countsA <- diff_counts[,c(1,3,5)]
get_density <- function(x, y, ...) {
dens <- MASS::kde2d(x, y, ...)
ix <- findInterval(x, dens$x)
iy <- findInterval(y, dens$y)
ii <- cbind(ix, iy)
return(dens$z[ii])
}
treat_avg$hour <- as.numeric(treat_avg$hour)
treat_avg$densityR <- get_density(treat_avg$hour, treat_avg$rubro.vs.substrate, n=40)
treat_avg$densityA <- get_density(treat_avg$hour, treat_avg$acre.vs.substrate, n=40)
ggplot(treat_avg) + geom_point(aes(treat_avg$hour, treat_avg$rubro.vs.substrate, size = treat_avg$densityR)) + scale_color_viridis() + ylim(-3.5,5.5) + ggtitle("Sedum rubrotinctum - Bare Substrate") + ylab("Temperature Difference") + xlab("Hour") + labs(size="Density") + geom_hline(yintercept=0, linetype="dashed", color = "red")
knitr::kable(diff_countsR, digits = 4, caption = "Table: Difference Score Counts for Sedum rubrotinctum")
ggplot(treat_avg) + theme_void()
ggplot(treat_avg) + geom_point(aes(treat_avg$hour, treat_avg$acre.vs.substrate, size = treat_avg$densityA)) + scale_color_viridis() + ylim(-3.5,5.5) + ggtitle("Sedum acre - Bare Substrate") + ylab("Temperature Difference") + xlab("Hour") + labs(size="Density") + geom_hline(yintercept=0, linetype="dashed", color = "red")
knitr::kable(diff_countsA, digits = 4, caption = "Table: Difference Score Counts for Sedum acre")
# Comparison of Temperatures by Hour
hrly_avg <-
treat_avg %>%
group_by(hour) %>%
summarize(mean(Sedum.rubro), mean(Sedum.acre), mean(bare.substrate))
hrly_avg <- hrly_avg[1:24,]
hrly_avg$rubro_diff <- hrly_avg$`mean(Sedum.rubro)`- hrly_avg$`mean(bare.substrate)`
hrly_avg$acre_diff <- hrly_avg$`mean(Sedum.acre)`- hrly_avg$`mean(bare.substrate)`
hrly_avg$rubro_diff <- signif(hrly_avg$rubro_diff, digits = 6)
hrly_avg$acre_diff <- signif(hrly_avg$acre_diff, digits = 6)
hrly_avg$`mean(bare.substrate)` <- signif(hrly_avg$`mean(bare.substrate)`, digits = 6)
hrly_avg$`mean(Sedum.rubro)` <- signif(hrly_avg$`mean(Sedum.rubro)`, digits = 6)
hrly_avg$`mean(Sedum.acre)` <- signif(hrly_avg$`mean(Sedum.acre)`, digits = 6)
plot(hrly_avg$hour, hrly_avg$`mean(Sedum.acre)`, type = "l", col = "blue",
main = "Hourly Temperature Averages",
xlab = "hour",
ylim = c(10,30),
ylab = "avg temperature (C)")
lines(hrly_avg$hour, hrly_avg$`mean(bare.substrate)`, col="black")
lines(hrly_avg$hour, hrly_avg$`mean(Sedum.rubro)`, col="red")
legend("topleft", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)
only_8am <-
treat_avg %>%
filter(hour == "8" | hour == "08") %>%
group_by(day) %>%
summarize(mean(bare.substrate), mean(Sedum.rubro), mean(Sedum.acre))
plot(only_8am$day, only_8am$`mean(bare.substrate)`, type = "l", main = "Daily Temperatures at 8am", xlab = "", ylab = "Temperature (C)")
lines(only_8am$day, only_8am$`mean(Sedum.rubro)`, type = "l", col = "red")
lines(only_8am$day, only_8am$`mean(Sedum.acre)`, type = "l", col = "blue")
legend("topleft", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)
only_daytime <-
treat_avg %>%
filter(hour > "10") %>%
filter(hour < "17") %>%
group_by(day) %>%
summarize(mean(bare.substrate), mean(Sedum.rubro), mean(Sedum.acre))
plot(only_daytime$day, only_daytime$`mean(bare.substrate)`, type = "l", main = "Daily Temperatures from 11am to 4pm", xlab = "", ylab = "Temperature (C)")
lines(only_daytime$day, only_daytime$`mean(Sedum.rubro)`, type = "l", col = "red")
lines(only_daytime$day, only_daytime$`mean(Sedum.acre)`, type = "l", col = "blue")
legend("topleft", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)
datatable(hrly_avg, class = 'cell-border stripe', options = list(pageLength = 24))
# Diurnal Temperature Ranges (DTR)
daily_range <-
treat_avg %>%
group_by(day) %>%
summarize(max(Sedum.rubro), min(Sedum.rubro), mean(Sedum.rubro), max(Sedum.acre), min(Sedum.acre), mean(Sedum.acre), max(bare.substrate), min(bare.substrate), mean(bare.substrate))
daily_range <-
daily_range %>%
mutate(rubro_range = `max(Sedum.rubro)` - `min(Sedum.rubro)`) %>%
mutate(acre_range = `max(Sedum.acre)` - `min(Sedum.acre)`) %>%
mutate(soil_range = `max(bare.substrate)` - `min(bare.substrate)`)
plot(daily_range$day, daily_range$rubro_range, type = "l", col = "red",
main = "Daily Temperature Ranges (Interior Sensors)",
xlab = "",
ylab = "Temperature Range (C)")
lines(daily_range$day, daily_range$acre_range, col="blue", lty = 1)
lines(daily_range$day, daily_range$soil_range, col="black", lty = 1)
legend("bottom", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)
DTR_summ <-
daily_range %>%
summarize(mean(rubro_range), mean(acre_range), mean(soil_range))
knitr::kable(DTR_summ, digits = 4, caption = "Table: Summary of Mean DTR for Each Treatment")
Count_types <- c("Smaller DTR", "Larger DTR", "Same DTR")
Rdtr_counts <- rbind(sum((daily_range$rubro_range - daily_range$soil_range) < 0), sum((daily_range$rubro_range - daily_range$soil_range) > 0), sum((daily_range$rubro_range - daily_range$soil_range) == 0))
Adtr_counts <- rbind(sum((daily_range$acre_range - daily_range$soil_range) < 0), sum((daily_range$acre_range - daily_range$soil_range) > 0), sum((daily_range$acre_range - daily_range$soil_range) == 0))
DTR_counts <- cbind.data.frame(Count_types, Rdtr_counts, Adtr_counts)
ggplot(treat_avg) + theme_void()
# Daily Max Temperatures
plot(daily_range$day, daily_range$`max(Sedum.rubro)`, type = "l", col = "red",
main = "Daily Max Temperature (Interior Sensors)",
xlab = "",
ylab = "Temperature (C)")
lines(daily_range$day, daily_range$`max(Sedum.acre)`, col="blue", lty = 1)
lines(daily_range$day, daily_range$`max(bare.substrate)`, col="black", lty = 1)
legend("bottom", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)
Category <- c("Lower Max (vs Soil)", "Higher Max (vs Soil)", "Same Max (vs Soil)", "Average Max Temperature", "Maximum Max Temperature")
rubro_max <- rbind(sum((daily_range$`max(Sedum.rubro)` - daily_range$`max(bare.substrate)`) < 0),
sum((daily_range$`max(Sedum.rubro)` - daily_range$`max(bare.substrate)`) > 0),
sum((daily_range$`max(Sedum.rubro)` - daily_range$`max(bare.substrate)`) == 0),
mean(daily_range$`max(Sedum.rubro)`),
max(daily_range$`max(Sedum.rubro)`))
acre_max <- rbind(sum((daily_range$`max(Sedum.acre)` - daily_range$`max(bare.substrate)`) < 0),
sum((daily_range$`max(Sedum.acre)` - daily_range$`max(bare.substrate)`) > 0),
sum((daily_range$`max(Sedum.acre)` - daily_range$`max(bare.substrate)`) == 0),
mean(daily_range$`max(Sedum.acre)`),
max(daily_range$`max(Sedum.acre)`))
Max_counts <- cbind.data.frame(Category, rubro_max, acre_max)
knitr::kable(Max_counts, digits = 3, caption = "Table: Summary of Maximum Temperature by Treatment")
ggplot(treat_avg) + theme_void()
# Daily Min Temperatures
plot(daily_range$day, daily_range$`min(Sedum.rubro)`, type = "l", col = "red",
main = "Daily Min Temperature (Interior Sensors)",
xlab = "",
ylab = "Temperature (C)",
ylim = c(5,16))
lines(daily_range$day, daily_range$`min(Sedum.acre)`, col="blue", lty = 1)
lines(daily_range$day, daily_range$`min(bare.substrate)`, col="black", lty = 1)
legend("bottom", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)
Category <- c("Lower Min (vs Soil)", "Higher Min (vs Soil)", "Same Min (vs Soil)", "Average Min Temperature", "Minimum Min Temperature")
rubro_max <- rbind(sum((daily_range$`min(Sedum.rubro)` - daily_range$`min(bare.substrate)`) < 0),
sum((daily_range$`min(Sedum.rubro)` - daily_range$`min(bare.substrate)`) > 0),
sum((daily_range$`min(Sedum.rubro)` - daily_range$`min(bare.substrate)`) == 0),
mean(daily_range$`min(Sedum.rubro)`),
min(daily_range$`min(Sedum.rubro)`))
acre_max <- rbind(sum((daily_range$`min(Sedum.acre)` - daily_range$`min(bare.substrate)`) < 0),
sum((daily_range$`min(Sedum.acre)` - daily_range$`min(bare.substrate)`) > 0),
sum((daily_range$`min(Sedum.acre)` - daily_range$`min(bare.substrate)`) == 0),
mean(daily_range$`min(Sedum.acre)`),
min(daily_range$`min(Sedum.acre)`))
Max_counts <- cbind.data.frame(Category, rubro_max, acre_max)
knitr::kable(Max_counts, digits = 3, caption = "Table: Summary of Minimum Temperature by Treatment")
ggplot(treat_avg) + theme_void()
t_test <- c("rubro DTR", "acre DTR", "rubro max", "acre max", "rubro min", "acre min")
p_value <- c(t.test(daily_range$rubro_range, daily_range$soil_range, paired = TRUE)$p.value,
t.test(daily_range$acre_range, daily_range$soil_range, paired = TRUE)$p.value,
t.test(daily_range$`max(Sedum.rubro)`, daily_range$`max(bare.substrate)`, paired = TRUE)$p.value,
t.test(daily_range$`max(Sedum.acre)`, daily_range$`max(bare.substrate)`, paired = TRUE)$p.value,
t.test(daily_range$`min(Sedum.rubro)`, daily_range$`min(bare.substrate)`, paired = TRUE)$p.value,
t.test(daily_range$`min(Sedum.acre)`, daily_range$`min(bare.substrate)`, paired = TRUE)$p.value)
CI_Lower <- c(t.test(daily_range$rubro_range, daily_range$soil_range, paired = TRUE)$conf.int[1],
t.test(daily_range$acre_range, daily_range$soil_range, paired = TRUE)$conf.int[1],
t.test(daily_range$`max(Sedum.rubro)`, daily_range$`max(bare.substrate)`, paired=TRUE)$conf.int[1],
t.test(daily_range$`max(Sedum.acre)`, daily_range$`max(bare.substrate)`, paired=TRUE)$conf.int[1],
t.test(daily_range$`min(Sedum.rubro)`, daily_range$`min(bare.substrate)`,paired=TRUE)$conf.int[1],
t.test(daily_range$`min(Sedum.acre)`, daily_range$`min(bare.substrate)`, paired=TRUE)$conf.int[1])
CI_Upper <- c(t.test(daily_range$rubro_range, daily_range$soil_range, paired = TRUE)$conf.int[2],
t.test(daily_range$acre_range, daily_range$soil_range, paired = TRUE)$conf.int[2],
t.test(daily_range$`max(Sedum.rubro)`, daily_range$`max(bare.substrate)`, paired=TRUE)$conf.int[2],
t.test(daily_range$`max(Sedum.acre)`, daily_range$`max(bare.substrate)`, paired=TRUE)$conf.int[2],
t.test(daily_range$`min(Sedum.rubro)`, daily_range$`min(bare.substrate)`,paired=TRUE)$conf.int[2],
t.test(daily_range$`min(Sedum.acre)`, daily_range$`min(bare.substrate)`, paired=TRUE)$conf.int[2])
ttest_pvals <- cbind.data.frame(t_test, p_value, CI_Lower, CI_Upper)
knitr::kable(ttest_pvals, digits = 4, caption = "Table: Summary of Paired T-tests for DTR, Min, and Max Temperatures (alpha = 0.05)")
# Linear Models for Treatment vs Control
ggplot(treat_avg, aes(x=bare.substrate, y=Sedum.rubro)) +
geom_point()+
geom_smooth(method = "lm")+
ylim(7.5,39)+xlim(7.5,39)+
ylab("sedum rubro")+
xlab("bare substrate")+
geom_abline(b=1, color="red", linetype=2)+
ggtitle("Linear Model of soil ~ Sedum rubrotinctum")
linearMod1 <- lm(bare.substrate ~ Sedum.rubro , data=treat_avg) %>%
summary()%>%
broom::tidy()
knitr::kable(linearMod1, digits = 4, caption = "Linear Model Summary Statistics: soil ~ Sedum rubrotinctum")
ggplot(treat_avg) + theme_void()
ggplot(treat_avg, aes(x=bare.substrate, y=Sedum.acre)) +
geom_point()+
geom_smooth(method = "lm")+
ylim(7.5,39)+xlim(7.5,39)+
ylab("sedum acre")+
xlab("bare substrate")+
geom_abline(b=1, color="red", linetype=2)+
ggtitle("Linear Model of soil ~ Sedum acre")
linearMod2 <- lm(bare.substrate ~ Sedum.acre , data=treat_avg) %>%
summary()%>%
broom::tidy()
knitr::kable(linearMod2, digits = 4, caption = "Linear Model Summary Statistics: soil ~ Sedum acre")
ggplot(treat_avg) + theme_void()
fit <- lm(bare.substrate ~ Sedum.rubro, data=treat_avg)
treat_avg$predicted <- predict(fit)
treat_avg$residuals <- residuals(fit)
ggplot(treat_avg, aes(x=bare.substrate, y=residuals)) +
geom_point(aes(color = abs(residuals)), size = 2) +
scale_color_continuous(low = "blue", high = "red") +
guides(color = FALSE) +
xlab("Bare Substrate Temperature") +
ylab("Residuals") +
geom_smooth(method = "lm", se = FALSE, color = "black") +
ggtitle("Sedum rubrotinctum residuals vs Bare Substrate")
fit <- lm(bare.substrate ~ Sedum.acre, data=treat_avg)
treat_avg$predicted <- predict(fit)
treat_avg$residuals <- residuals(fit)
ggplot(treat_avg, aes(x=bare.substrate, y=residuals)) +
geom_point(aes(color = abs(residuals)), size = 2) +
scale_color_continuous(low = "blue", high = "red") +
guides(color = FALSE) +
xlab("Bare Substrate Temperature") +
ylab("Residuals") +
geom_smooth(method = "lm", se = FALSE, color = "black") +
ggtitle("Sedum acre residuals vs Bare Substrate")
ggplot(treat_avg) + theme_void()
ggplot(treat_avg, aes(x=bare.substrate, y=rubro.vs.substrate)) +
geom_point()+
geom_smooth()+
ylab("sedum rubro. - bare substrate")+
xlab("bare substrate")+
ggtitle("Loess regression of soil ~ (Sedum rubrotinctum - soil)")
linearMod3 <- lm(bare.substrate ~ rubro.vs.substrate, data=treat_avg) %>%
summary() %>%
broom::tidy()
knitr::kable(linearMod3, digits = 4, caption = "Linear Model Summary Statistics")
ggplot(treat_avg) + theme_void()
ggplot(treat_avg, aes(x=bare.substrate, y=acre.vs.substrate)) +
geom_point()+
geom_smooth()+
ylab("sedum acre - bare substrate")+
xlab("bare substrate")+
ggtitle("Loess regression of soil ~ (Sedum acre - soil)")
linearMod4 <- lm(bare.substrate ~ acre.vs.substrate, data=treat_avg) %>%
summary() %>%
broom::tidy()
knitr::kable(linearMod4, digits = 4, caption = "Linear Model Summary Statistics")
# When Ambient > 25 degrees C (Interior T)
high_t <-
all_cells %>%
filter(Ambient > 25) %>%
filter(Location == "interior")
sum_hiT <-
dplyr::group_by(high_t, Treatment) %>%
dplyr::summarize(
count = n(),
max = max(Temp),
min = min(Temp),
range = (max(Temp) - min(Temp)),
mean = mean(Temp, na.rm = TRUE),
median = median(Temp, na.rm = TRUE),
sd = sd(Temp, na.rm = TRUE)
)
ggboxplot(high_t, x = "Treatment", y = "Temp",
color = "Treatment", palette = c("#00AFBB", "#E7B800", "#FC4E07"),
order = c("sedum rubrotinctum", "sedum acre", "bare substrate"),
ylab = "Temperature",
xlab = FALSE,
main = "Interior Sensor Temperature when Ambient is Above 25 C",
legend = "",
label.rectangle = TRUE)
knitr::kable(sum_hiT, digits = 4, caption = "Table: Summary of High (>25) Ambient Temperatures")
# Normality Tests
ggdensity(treat_avg$Sedum.rubro,
main = "Density plot of Sedum rubrotinctum Temperature",
xlab = "Sample")
ggqqplot(treat_avg$Sedum.rubro)
shapiro.test(treat_avg$Sedum.rubro)
ggdensity(treat_avg$Sedum.acre,
main = "Density plot of Sedum acre Temperature",
xlab = "Sample")
ggqqplot(treat_avg$Sedum.acre)
shapiro.test(treat_avg$Sedum.acre)
#Sedum rubrotinctum Transformations
rubro <- treat_avg$Sedum.rubro
par(mfrow=c(2,3))
#1. No Transformation
plotNormalHistogram(rubro, main = "No Transformation", xlab = "")
#2. Square Root Transformation
T_sqrt = sqrt(rubro)
plotNormalHistogram(T_sqrt, main = "Square Root", xlab = "")
#3. Cube Root Transformation
T_cub = sign(rubro) * abs(rubro)^(1/3)
plotNormalHistogram(T_cub, main = "Cube Root", xlab = "")
#4. Log Transformation
T_log = log(rubro)
plotNormalHistogram(T_log, main = "Log", xlab = "")
#5. Tukey's Ladder of Powers Transformation
T_tuk <- transformTukey(rubro, plotit=FALSE, quiet = TRUE)
plotNormalHistogram(T_tuk, main = "Tukey's Ladder of Powers", xlab = "")
#6. Box-Cox Transformation
invisible(powerTransform(rubro))
lambda <- -0.2877828
T_box <- (rubro ^ lambda - 1)/lambda
plotNormalHistogram(T_box, main = "Box-Cox", xlab = "")
skews <- c(signif(skewness(rubro), digits = 3),
signif(skewness(T_sqrt), digits = 3),
signif(skewness(T_cub), digits = 3),
signif(skewness(T_log), digits = 3),
signif(skewness(T_tuk), digits = 3),
signif(skewness(T_box), digits = 3))
kurtos <- c(signif(kurtosis(rubro), digits = 3),
signif(kurtosis(T_sqrt), digits = 3),
signif(kurtosis(T_cub), digits = 3),
signif(kurtosis(T_log), digits = 3),
signif(kurtosis(T_tuk), digits = 3),
signif(kurtosis(T_box), digits = 3))
names <- c("No Transformation", "Square Root", "Cube Root", "Log", "Tukey's Ladder of Powers", "Box-Cox")
distList <- cbind.data.frame(names, skews, kurtos)
colnames(distList) <- c("Transformation Type", "Skewness", "Kurtosis")
knitr::kable(distList, caption = "Table: Skewness + Kurtosis")
ggplot(treat_avg) + theme_void()
#Sedum acre Transformations
acre <- treat_avg$Sedum.acre
par(mfrow=c(2,3))
#1. No Transformation
plotNormalHistogram(acre, main = "No Transformation", xlab = "")
#2. Square Root Transformation
T_sqrt = sqrt(acre)
plotNormalHistogram(T_sqrt, main = "Square Root", xlab = "")
#3. Cube Root Transformation
T_cub = sign(acre) * abs(acre)^(1/3)
plotNormalHistogram(T_cub, main = "Cube Root", xlab = "")
#4. Log Transformation
T_log = log(acre)
plotNormalHistogram(T_log, main = "Log", xlab = "")
#5. Tukey's Ladder of Powers Transformation
T_tuk <- transformTukey(acre, plotit=FALSE, quiet = TRUE)
plotNormalHistogram(T_tuk, main = "Tukey's Ladder of Powers", xlab = "")
#6. Box-Cox Transformation
invisible(powerTransform(acre))
lambda <- -0.2294328
T_box <- (acre ^ lambda - 1)/lambda
plotNormalHistogram(T_box, main = "Box-Cox", xlab = "")
skews <- c(signif(skewness(acre), digits = 3),
signif(skewness(T_sqrt), digits = 3),
signif(skewness(T_cub), digits = 3),
signif(skewness(T_log), digits = 3),
signif(skewness(T_tuk), digits = 3),
signif(skewness(T_box), digits = 3))
kurtos <- c(signif(kurtosis(acre), digits = 3),
signif(kurtosis(T_sqrt), digits = 3),
signif(kurtosis(T_cub), digits = 3),
signif(kurtosis(T_log), digits = 3),
signif(kurtosis(T_tuk), digits = 3),
signif(kurtosis(T_box), digits = 3))
names <- c("No Transformation", "Square Root", "Cube Root", "Log", "Tukey's Ladder of Powers", "Box-Cox")
distList <- cbind.data.frame(names, skews, kurtos)
colnames(distList) <- c("Transformation Type", "Skewness", "Kurtosis")
knitr::kable(distList, caption = "Table: Skewness + Kurtosis")
# Appendix - Code